Problem: Simplify the following expression: $p = \dfrac{-10a - 50}{45a + 35}$ You can assume $a \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-10a - 50 = - (2\cdot5 \cdot a) - (2\cdot5\cdot5)$ The denominator can be factored: $45a + 35 = (3\cdot3\cdot5 \cdot a) + (5\cdot7)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $p = \dfrac{(5)(-2a - 10)}{(5)(9a + 7)}$ Dividing both the numerator and denominator by $5$ gives: $p = \dfrac{-2a - 10}{9a + 7}$